Question

find the factorisation of (x–y)^3+8(x+y)^3​

Answer 1

Answer:

a3−b3=(a−b)(a2+ab+b2)

Also, we know that 8=23

and a3b3=(ab)3

So (x−y)3−8(x+y)3

= (x−y)3−(2x+2y)3

=[(x−y)−(2x+2y)][(x−y)2+(x−y)(2x+2y)+(2x+2y)2]

= (−x−3y)[bigmess]

The big mess takes some care to manage the algebra without mistakes. We will have x^2s, xys, and y^2s involved.

7x^{2} + 6xy + 3y^{2}

So

= (−x−3y)[7x2+6xy+3y2]

Answer 2

Step-by-step explanation:

(x-y) ^3-8(x+y) ^3?

We have a nifty little rule that

a3−b3=(a−b)(a2+ab+b2)

Also, we know that 8=23

and a3b3=(ab)3

So (x−y)3−8(x+y)3

= (x−y)3−(2x+2y)3

= [(x−y)−(2x+2y)][(x−y)2+(x−y)(2x+2y)+(2x+2y)2]